Subgroups — C₂×#10596290 #11918487

Order 1152.

4380 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×#41	C₂	1	1	yes	maximal, characteristic
2	#10596290	C₂	1	16	yes	maximal, direct product factor
3	C₂×#64157	C₂	1	8	yes	maximal, complemented
4	C₂²×#3748	C₂	1	6	yes	maximal, complemented
5	C₂×#5819	—	3	4	no	maximal
6	C₂×C₃²×#41	C₄	1	4	yes	—
7	C₂×C₃²×#41	C₄	1	8	yes	—
8	C₂×C₃²×#41	C₂²	1	4	yes	—
9	C₂×C₃²×#41	C₂²	1	8	yes	—
10	C₂²×C₃²×Q₈	C₄	1	1	yes	characteristic
11	C₂²×C₃²×D₄	C₄	1	3	yes	—
12	C₂³×C₃²×C₄	C₂²	1	3	yes	—
13	#64157	C₂²	1	64	yes	complemented
14	C₂×#3748	C₂²	1	4	yes	—
15	C₂×#3748	C₂²	1	12	yes	complemented
16	C₂×#3748	C₂²	1	48	yes	complemented
17	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	12	yes	complemented
18	C₂²×C₃×#41	D₃	1	4	yes	—
19	#5819	—	3	64	no	—
20	C₂×#948	—	3	32	no	—
21	C₂²×#208	—	3	24	no	—
22	C₂⁴×C₃²	C₂×C₄	1	3	yes	—
23	C₃²×#41	C₂×C₄	1	16	yes	—
24	C₃²×#41	C₂×C₄	1	32	yes	—
25	C₃²×#41	C₂³	1	16	yes	—
26	C₂×C₃²×Q₈	C₂×C₄	1	4	yes	—
27	C₂×C₃²×Q₈	C₂×C₄	1	8	yes	—
28	C₂×C₃²×D₄	C₂×C₄	1	12	yes	—
29	C₂×C₃²×D₄	C₂×C₄	1	24	yes	—
30	C₂²×C₃²×C₄	C₂×C₄	1	3	yes	—
31	C₂²×C₃²×C₄	C₂×C₄	1	6	yes	—
32	C₂²×C₃²×C₄	C₂×C₄	1	12	yes	—
33	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
34	C₂²×C₃²×C₄	C₂³	1	6	yes	—
35	C₂²×C₃²×C₄	C₂³	1	12	yes	—
36	#3748	C₂³	1	16	yes	—
37	#3748	C₂³	1	48	yes	complemented
38	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	8	yes	—
39	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	48	yes	complemented
40	C₂×#568	—	9	1	no	Sylow
41	C₂×C₃×#41	Dic₃	1	16	yes	—
42	C₂×C₃×#41	Dic₃	1	32	yes	—
43	C₂×C₃×#41	C₂×D₃	1	16	yes	—
44	C₂×C₃×#41	C₂×D₃	1	32	yes	—
45	C₂²×C₃×Q₈	Dic₃	1	4	yes	—
46	C₂²×C₃×D₄	Dic₃	1	12	yes	—
47	C₂³×C₃×C₄	C₂×D₃	1	12	yes	—
48	#948	—	3	256	no	—
49	C₂×#208	—	3	16	no	—
50	C₂×#208	—	3	48	no	—
51	C₂×#208	—	3	192	no	—
52	C₂²×C₃⋊C₈	—	3	48	no	—
53	C₂³×C₃²	—	4	6	no	—
54	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
55	C₂³×C₃²	C₂²×C₄	1	6	yes	—
56	C₂³×C₃²	C₂²×C₄	1	12	yes	—
57	C₃²×Q₈	C₂²×C₄	1	16	yes	—
58	C₃²×D₄	C₂²×C₄	1	48	yes	—
59	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
60	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₃²×C₄	C₂²×C₄	1	12	yes	—
62	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
63	C₂×C₃²×C₄	C₂²×C₄	1	12	yes	—
64	C₂×C₃²×C₄	C₂²×C₄	1	24	yes	—
65	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
66	C₂×C₃²×C₄	C₂⁴	1	12	yes	—
67	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
68	C₃⋊(C₃⋊C₈)	C₂⁴	1	16	yes	—
69	C₂²×#41	C₃⋊D₃	1	1	yes	characteristic
70	#568	—	9	16	no	—
71	C₂×#131	—	9	8	no	—
72	C₂²×M₁₆	—	9	6	no	—
73	C₂⁴×C₃	C₂×Dic₃	1	12	yes	—
74	C₃×#41	C₂×Dic₃	1	64	yes	—
75	C₃×#41	C₂×Dic₃	1	128	yes	—
76	C₃×#41	C₂²×D₃	1	64	yes	—
77	C₂×C₃×Q₈	C₂×Dic₃	1	16	yes	—
78	C₂×C₃×Q₈	C₂×Dic₃	1	32	yes	—
79	C₂×C₃×D₄	C₂×Dic₃	1	48	yes	—
80	C₂×C₃×D₄	C₂×Dic₃	1	96	yes	—
81	C₂²×C₃×C₄	C₂×Dic₃	1	12	yes	—
82	C₂²×C₃×C₄	C₂×Dic₃	1	24	yes	—
83	C₂²×C₃×C₄	C₂×Dic₃	1	48	yes	—
84	C₂²×C₃×C₄	C₂²×D₃	1	24	yes	—
85	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
86	C₂²×C₃×C₄	C₂²×D₃	1	48	yes	—
87	#208	—	3	64	no	—
88	#208	—	3	192	no	—
89	C₂×C₃⋊C₈	—	3	32	no	—
90	C₂×C₃⋊C₈	—	3	192	no	—
91	C₂²×C₃²	—	2	2	no	—
92	C₂²×C₃²	—	2	12	no	—
93	C₂²×C₃²	—	4	12	no	—
94	C₂²×C₃²	C₂³×C₄	1	2	yes	—
95	C₂²×C₃²	C₂³×C₄	1	12	yes	—
96	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
97	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
98	C₃²×C₄	C₂³×C₄	1	2	yes	—
99	C₃²×C₄	C₂³×C₄	1	12	yes	—
100	C₃²×C₄	C₂⁵	1	1	yes	characteristic
101	C₂×#41	C₃⋊Dic₃	1	4	yes	—
102	C₂×#41	C₃⋊Dic₃	1	8	yes	—
103	C₂×#41	C₂×C₃⋊D₃	1	4	yes	—
104	C₂×#41	C₂×C₃⋊D₃	1	8	yes	—
105	C₂²×Q₈	C₃⋊Dic₃	1	1	yes	characteristic
106	C₂²×D₄	C₃⋊Dic₃	1	3	yes	—
107	C₂³×C₄	C₂×C₃⋊D₃	1	3	yes	—
108	#131	—	9	64	no	—
109	C₂×M₁₆	—	9	4	no	—
110	C₂×M₁₆	—	9	12	no	—
111	C₂×M₁₆	—	9	48	no	—
112	C₂²×C₈	—	9	12	no	—
113	C₂³×C₃	—	4	24	no	—
114	C₂³×C₃	C₂²×Dic₃	1	4	yes	—
115	C₂³×C₃	C₂²×Dic₃	1	24	yes	—
116	C₂³×C₃	C₂²×Dic₃	1	48	yes	—
117	C₃×Q₈	C₂²×Dic₃	1	64	yes	—
118	C₃×D₄	C₂²×Dic₃	1	192	yes	—
119	C₂×C₃×C₄	C₂²×Dic₃	1	8	yes	—
120	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
121	C₂×C₃×C₄	C₂²×Dic₃	1	48	yes	—
122	C₂×C₃×C₄	C₂²×Dic₃	1	24	yes	—
123	C₂×C₃×C₄	C₂²×Dic₃	1	48	yes	—
124	C₂×C₃×C₄	C₂²×Dic₃	1	96	yes	—
125	C₂×C₃×C₄	C₂³×D₃	1	48	yes	—
126	C₂×C₃×C₄	C₂³×D₃	1	8	yes	—
127	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
128	C₃⋊C₈	—	3	64	no	—
129	C₂×C₃²	—	2	2	no	—
130	C₂×C₃²	—	2	12	no	—
131	C₂×C₃²	#568	1	2	yes	complemented
132	C₂×C₃²	C₂⁴×C₄	1	1	yes	characteristic
133	C₂⁴	C₂×C₃⋊Dic₃	1	3	yes	—
134	#41	C₂×C₃⋊Dic₃	1	16	yes	—
135	#41	C₂×C₃⋊Dic₃	1	32	yes	—
136	#41	C₂²×C₃⋊D₃	1	16	yes	—
137	C₂×Q₈	C₂×C₃⋊Dic₃	1	4	yes	—
138	C₂×Q₈	C₂×C₃⋊Dic₃	1	8	yes	—
139	C₂×D₄	C₂×C₃⋊Dic₃	1	12	yes	—
140	C₂×D₄	C₂×C₃⋊Dic₃	1	24	yes	—
141	C₂²×C₄	C₂×C₃⋊Dic₃	1	3	yes	—
142	C₂²×C₄	C₂×C₃⋊Dic₃	1	6	yes	—
143	C₂²×C₄	C₂×C₃⋊Dic₃	1	12	yes	—
144	C₂²×C₄	C₂²×C₃⋊D₃	1	12	yes	—
145	C₂²×C₄	C₂²×C₃⋊D₃	1	6	yes	—
146	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
147	M₁₆	—	9	16	no	—
148	M₁₆	—	9	48	no	—
149	C₂×C₈	—	9	48	no	—
150	C₂×C₈	—	9	8	no	—
151	C₂²×C₃	—	2	8	no	—
152	C₂²×C₃	—	2	48	no	—
153	C₂²×C₃	—	4	48	no	—
154	C₂²×C₃	C₂³×Dic₃	1	8	yes	—
155	C₂²×C₃	C₂³×Dic₃	1	48	yes	—
156	C₂²×C₃	C₂³×Dic₃	1	4	yes	—
157	C₃×C₄	C₂³×Dic₃	1	8	yes	—
158	C₃×C₄	C₂³×Dic₃	1	4	yes	—
159	C₃×C₄	C₂³×Dic₃	1	48	yes	—
160	C₃×C₄	C₂⁴×D₃	1	4	yes	—
161	C₃²	C₂×#568	1	1	yes	characteristic, complemented, Sylow
162	C₂³	—	4	6	no	—
163	C₂³	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
164	C₂³	C₂²×C₃⋊Dic₃	1	6	yes	—
165	C₂³	C₂²×C₃⋊Dic₃	1	12	yes	—
166	Q₈	C₂²×C₃⋊Dic₃	1	16	yes	—
167	D₄	C₂²×C₃⋊Dic₃	1	48	yes	—
168	C₂×C₄	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
169	C₂×C₄	C₂²×C₃⋊Dic₃	1	2	yes	—
170	C₂×C₄	C₂²×C₃⋊Dic₃	1	12	yes	—
171	C₂×C₄	C₂²×C₃⋊Dic₃	1	6	yes	—
172	C₂×C₄	C₂²×C₃⋊Dic₃	1	24	yes	—
173	C₂×C₄	C₂²×C₃⋊Dic₃	1	12	yes	—
174	C₂×C₄	C₂³×C₃⋊D₃	1	12	yes	—
175	C₂×C₄	C₂³×C₃⋊D₃	1	2	yes	—
176	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
177	C₈	—	9	16	no	—
178	C₂×C₃	—	2	8	no	—
179	C₂×C₃	—	2	48	no	—
180	C₂×C₃	#5819	1	8	yes	complemented
181	C₂×C₃	C₂⁴×Dic₃	1	4	yes	—
182	C₂²	—	2	2	no	—
183	C₂²	—	2	12	no	—
184	C₂²	—	4	12	no	—
185	C₂²	C₂³×C₃⋊Dic₃	1	2	yes	—
186	C₂²	C₂³×C₃⋊Dic₃	1	12	yes	—
187	C₂²	C₂³×C₃⋊Dic₃	1	1	yes	characteristic
188	C₄	C₂³×C₃⋊Dic₃	1	2	yes	—
189	C₄	C₂³×C₃⋊Dic₃	1	12	yes	—
190	C₄	C₂³×C₃⋊Dic₃	1	1	yes	characteristic
191	C₄	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
192	C₃	C₂×#5819	1	4	yes	complemented
193	C₂	—	2	2	no	—
194	C₂	—	2	12	no	—
195	C₂	#10596290	1	2	yes	direct product factor
196	C₂	C₂⁴×C₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×C₃⋊D₃
commutator	C₂×C₃²	C₂⁴×C₄
Frattini	C₄	C₂⁴×C₃⋊D₃
Fitting, prime radical	C₂²×C₃²×#41	C₂
socle	C₂²×C₃²	C₂³×C₄
cosocle	C₃²×C₄	C₂⁵
hypercenter	C₂²×#41	C₃⋊D₃
hypocenter	C₃²	C₂×#568
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #10596290	C₂	direct (N × H)
3. C₂×#64157	C₂	semidirect
4. C₂²×#3748	C₂	semidirect
13. #64157	C₂²	semidirect
15. C₂×#3748	C₂²	semidirect
16. C₂×#3748	C₂²	semidirect
17. C₂²×C₃⋊(C₃⋊C₈)	C₂²	semidirect
37. #3748	C₂³	semidirect
39. C₂×C₃⋊(C₃⋊C₈)	C₂³	semidirect
131. C₂×C₃²	#568	semidirect
161. C₃²	C₂×#568	semidirect
180. C₂×C₃	#5819	semidirect
192. C₃	C₂×#5819	semidirect
195. C₂	#10596290	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃²×#41	2
#10596290	2
C₂×#64157	2
C₂²×#3748	2
C₂×#5819	3

Subgroups — C2×#10596290 #11918487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10596290 #11918487